
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 138, Pages 82–98
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This article is cited in 4 scientific papers (total in 4 papers)
On general production of entropy in open Markov quantum systems
A. S. Trushechkin^{abc} ^{a} Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^{b} National Engineering Physics Institute "MEPhI", Moscow
^{c} National University of Science and Technology «MISIS»
Abstract:
We discuss production of entropy per unit time for a quantum system
governed by the Lindblad equation. The difficulty is as follows: in order
to determine the total production of entropy, one must know the entropy
flow from the system into the environment. This requires additional
information on the environment and on its interaction with the system. The
Lindblad equation for the reduced density matrix of the system does not
contain such information. Therefore, the following question arises: What
minimum additional information about the environment must be added to the
Lindblad equation in order to find the flow of entropy into the environment
and the total production of entropy? To answer this question, we use the
concept of a complementary quantum channel known from the the quantum
information theory. We also prove a theorem on the nonnegativity of
production of entropy, and, under certain assumptions, the adiabatic and
nonadiabatic contribution to it.
Keywords:
open quantum systems, Lindblad equation, production of entropy, second law of thermodynamics.
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English version:
Journal of Mathematical Sciences, 2019, 241:2, 191–209
Bibliographic databases:
UDC:
517.958:530.145, 536.73, 536.75
MSC: 81S22, 82C10
Citation:
A. S. Trushechkin, “On general production of entropy in open Markov quantum systems”, Quantum computing, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 82–98; Journal of Mathematical Sciences, 241:2 (2019), 191–209
Citation in format AMSBIB
\Bibitem{Tru17}
\by A.~S.~Trushechkin
\paper On general production of entropy in open Markov quantum systems
\inbook Quantum computing
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 138
\pages 8298
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into216}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3801253}
\zmath{https://zbmath.org/?q=an:1426.81045}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 2
\pages 191209
\crossref{https://doi.org/10.1007/s10958019044174}
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This publication is cited in the following articles:

A. E. Teretenkov, “Quadratic Fermionic Dynamics with Dissipation”, Math. Notes, 102:6 (2017), 846–854

A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271

A. E. Teretenkov, “Dynamics of Moments for Quadratic GKSL Generators”, Math. Notes, 106:1 (2019), 151–155

A. S. Trushechkin, “Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems”, Proc. Steklov Inst. Math., 306 (2019), 257–270

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